library("TDA")

# create data set containing 100 randomly choosen 
# points from a circle of radius r = 1
circle1 = circleUnif(100, r = 1)


# create 2x2 matrix
A <- matrix(c(1, 2, 2, 0), nrow=2, ncol=2) 
C <- t(circle1)  # take the transpose of A
M <- A %*% C     # multiply A and C
E <- eigen(A)    # calculate eigenvalues and eigenvectors of A
E                # display E (note its data structure)
?E


plot(t(M), asp=1)  # note M is the image of circle C under map A
# Add an eigenvector to this plot (red asterisk)

#points(c(0,E$values[1]*E$vectors[1,1]),c(0,E$values[1]*E$vectors[2,1]))
arrows(0,0,E$values[1]*E$vectors[1,1],E$values[1]*E$vectors[2,1], col="red", lwd = 3)

#points(c(0,E$values[2]*E$vectors[1,2]),c(0,E$values[2]*E$vectors[2,2]))
arrows(0,0,E$values[2]*E$vectors[1,2],E$values[2]*E$vectors[2,2], col="blue", lwd = 3)


plot(t(M), asp=1)  # note M is the image of circle C under map A
# Add an eigenvector to this plot (red asterisk)
points(t(E$values[1]*E$vectors[,1]), pch=8, cex = 2, col=rgb(1, 0, 0))
# Add another eigenvector to this plot (blue asterisk)
points(t(E$values[2]*E$vectors[,2]), pch=8, cex = 2, col=rgb(0, 0, 1))
# Add origin (0, 0) to plot (green +).
points(t(c(0, 0)), pch=3, cex = 2, col=rgb(0, 1, 0))


E$vectors[,1]
A %*% E$vectors[,1]

E$values[1] * E$vectors[,1] - A %*% E$vectors[,1]
E$values[1]

abline(a=0, b=1)

sphere <- sphereUnif(100, 2, r = 1)
disk1 <- subset(sphere, select = -c(3) )
disk2 <- cbind(disk1[,1] + 4, disk1[,2])
disk3 <- cbind(disk1[,1], disk1[,2] + 4)
disk4 <- disk1 + 4
noise1 <- cbind(runif(100, -1,5), runif(100, -1,5))

noisy_disk <- rbind(disk1, disk2, disk3, disk4, noise1)
plot(noisy_disk, asp = 1)

line <- cbind(runif(40, -.1,.1), runif(40, 1,3))
new <- rbind(noisy_disk, line)
plot(new, asp = 1)